BEIRUT — Simultaneous attacks on the Islamic State-held cities of Mosul in Iraq and Raqqa, the de facto capital of the militant group’s self-proclaimed caliphate across the border in Syria, would make military sense: such assaults would make it harder for the extremists to move reinforcements and deny them a safe haven.

When preparing for the Mosul operations this summer, U.S. officials said a push against IS in Raqqa could be almost simultaneous, putting additional pressure on the group by stretching its ability to defend two strongholds at once.

While the long-awaited Mosul offensive began earlier this week, there’s no sign of an imminent campaign against Raqqa.

Perhaps that’s because Syria is proving to be a more daunting terrain than Iraq. Going after IS-held Raqqa would mean moving deeper into an explosive mix of regional and international rivalries, including a proxy war that has pitted the United States against Russia and its allies.

The fight against IS in northeastern Syria also underlines a U.S. reliance on its one effective partner there— Syria’s Kurds. Such an alliance for a Raqqa campaign threatens to ignite a new conflict, with another U.S. partner, NATO member Turkey, and its allied Syrian rebels.

In Iraq, the U.S. offers logistical and other support for the military in its fight against IS.

In Syria, Washington views President Bashar Assad’s government as illegitimate and cannot partner with him.

Even if IS were to be driven out of Raqqa, finding someone to administer the city would be problematic, said Noah Bonsey, a Syria expert with the International Crisis Group think tank.

Mosul is the largest city under IS control, with an estimated population of up to one million and no more than 10,000 fighters. Oil-rich Raqqa is home to nearly 200,000 people, most Sunni Arabs, and an estimated 5,000 militants.

Bonsey said retaking Raqqa is key to defeating IS militarily, a U.S. priority, but that among the warring factions in Syria “everybody else has other geostrategic interests that take higher priority.”

In recent weeks, U.S.-led coalition airstrikes targeted half a dozen bridges in Syria’s largely IS-controlled Deir el-Zour province between Raqqa and the Iraqi border. The strikes were aimed at cutting the road between Iraq and Syria for fleeing militants.

Activist Hussam Eesa reported increased IS activity in Raqqa, including more night-time checkpoints, and said some wounded and IS families arrived from Mosul before the start of the offensive. He said there was no sign of panic in Raqqa. Most fortifications in Raqqa, such as trenches, were built long ago, said Eesa, who is not in the city and whose group, Raqqa Is Being Slaughtered Silently, relies on leaked reports from residents.

Raqqa could serve as a refuge for IS fighters fleeing Mosul, even if roads are harder to access, said Jennifer Cafarella of the Washington-based Institute for the Study of War. Retreating fighters could also hide among fleeing civilians, or travel in small groups to evade coalition aircraft, she said. Others could withdraw to desert areas between Syria and Iraq for staging future attacks.

Since the summer’s discussions in Washington about a possible double-strike against IS, Turkey has entered the fray. Starting in August, Ankara has backed Syrian opposition fighters with tanks and aircraft.

This has complicated planning for a possible Raqqa campaign and threatened America’s main ally on the ground, the Kurds.

The rivalries are dangerous because IS is deft at exploiting divisions among its enemies, said Cafarella.

Kurdish fighters, mostly the well-trained and highly organized People’s Protection Units, or YPG, have been the U.S. partner in the anti-IS fight in Syria since 2015 when they freed the town of Kobani.